Brent crude climbed to $106.77 a barrel on Tuesday, up $1.49 or 1.4%, as the diplomatic standoff over the Strait of Hormuz showed no sign of breaking and US President Donald Trump flatly rejected reports he had offered Iran sanctions relief to end the seven-month war.

Trump wrote on Truth Social on Monday: "This is untrue. I offered them NOTHING." His post answered Axios and CNN reports citing unidentified US officials, who said the president was willing to ease sanctions and release frozen Iranian funds in exchange for "concrete progress" on Iran's nuclear program.

For shipowners and charterers, the more consequential signal came from Tehran. Iranian Foreign Minister Abbas Araqchi framed any reopening of the Strait of Hormuz — the chokepoint that normally carries roughly a fifth of globally traded oil — as conditional on a negotiated settlement. "Our conditions are clear, and any move toward reopening the Strait of Hormuz is contingent on these conditions being met," Araqchi posted on social media on Sunday. "Only a negotiated solution can get them out of this deadlock."

That positions the strait's reopening, rather than a ceasefire alone, as the variable that matters for tanker availability, war-risk premiums and Gulf loadings — none of which show signs of normalizing soon.

US and Iranian officials spoke separately with mediators on Monday as part of a renewed push to end the conflict, according to officials of both countries. Araqchi told reporters at the UN on Friday that the proposed deal would trigger a seven-day countdown to reopening the strait and a pause in regional fighting.

Trump rejected that framework outright on Saturday. "They want to make a deal to open the Hormuz Strait immediately because they're losing so badly," he told reporters at the White House, arguing desperation was driving the Iranian push for an agreement on the waterway. Araqchi responded that mediators had not officially relayed any US rejection: "We are waiting for the mediators to convey the definitive views to us, and we will make a decision based on them."

Iranian President Masoud Pezeshkian, speaking on CBS's "Face the Nation," said Tehran was ready for talks on its nuclear program and other issues, but not under duress. "Iran is not seeking war, but will defend itself against pressure, threats and attacks," Pezeshkian said, adding that Iran had already agreed "we're not supposed to develop nuclear weapons." Iran does not possess nuclear weapons and denies seeking them, while asserting a right to domestic nuclear energy capacity.

Trump has defined the war's goals as preventing Iran from acquiring a nuclear bomb, ending its ability to attack its neighbors, and creating conditions for Iranians to change their leadership.

The war — launched by Trump alongside Israel in February as "Operation Epic Fury" — has killed thousands and severely disrupted global energy supplies. Iran has struck US allies in the Gulf with drones and missiles, while its Houthi allies in Yemen have hit Saudi interests.

The Saudi angle is deteriorating. Houthi fighters have advanced in Yemen this month, routing forces of the Saudi-backed government and threatening Saudi oil exports through the Red Sea. That extends the risk map beyond Hormuz to the Bab el-Mandeb corridor, compounding the rerouting costs carriers and cargo owners have absorbed since the conflict began.

Oil markets absorbed the message. Brent and US West Texas Intermediate each closed nearly $1 a barrel higher in the previous session, and Tuesday's gains marked a second consecutive rise as supply concerns outweighed signs of recovering crude exports from the region. US WTI traded at $93.94, up $1.34 or 1.5%.

Verification of events in and around Hormuz is itself degrading. Reports of vessel strikes are surfacing days late, raising questions about how much of the fighting is going unrecorded and leaving operators pricing risk on incomplete information.

With Washington and Tehran both publicly refusing the other's terms, and Araqchi insisting Iran's conditions must be met before the strait reopens, freight and energy markets should expect elevated war-risk pricing and constrained Gulf tonnage to persist until mediators deliver a framework both sides accept.